At this stage, it is not obvious to make contact with the fixed points obtained in the previous truncation. The standard way to highlight these relation is to consider truncation with higher and higher valence, and seek convergence of the fixed points. But in our case, the difficulty of a such computations is very improved by the non-locality of the interactions, and these conclusions have to be confirmed by more finer analysis.
Let us remark that the study of the critical exponent [1]} could upset our analysis for the choice of the truncations with valances greater than 6. For instance, the fixed point \(FP_5\)  leads to a very large critical exponent and this can help to show that the truncation in this order remains non consistent. For the fixed point \(FP_{10}\)  the critical exponent is small, and adding another interaction of valence more than 8 becomes unnecessary.
Unlike, the fixed point \(FP_{10}\)  exhibits several relevant directions and these do not appear in the previous section by using just the truncation with interaction of valence 6.
